The Greek philosopher Heraclitus stated that the “only thing that is constant is change.” However, meaningful change rarely unfolds in straight lines but typically follow the Sigmoid Curve (S-fxn) shape of the power law.  The ‘slow, fast, slow’ structure of the curve describes a vast range120818_stacked_s-curves-thumb-600x358-2254.jpg of natural and historical phenomenon.  Evolution, epidemics, computers, and earthquakes can all be explained by the sigmoid curve. Joseph Schumpeter’s creative destruction is an example of a S-curve. Thomas Kuhn’s paradigm shifts in science can be explained by S-curves. The S-fxn is related to the bell curve via a differential. The “slow, fast, slow” becomes the “low, high, low.” Add a series of staggered upward and downward S curves, and you create a sine wave. 

The universe is filled with S curves but by definition, the nature of the relationship makes them mostly invisible to us. In a phase transition, an event is more surprising the longer we have been waiting for it, and maximally surprising, right before it happens. The physicist Al Bartlett stated that the “greatest shortcoming of the human race is our inability to understand the exponential function.” The ability to identify S-curves is an essential component of forecasting. We often overestimate the short term by miscalculating the speed at which the inflection point arrives and underestimate the long term. Furthermore, these relationships are often fractal in nature as identifying an S-curve relationship often signals the presence of smaller precisely defined and linked S curves.  

On a personal level, learning, skill building, expertise development all follow the S curve – slow, fast, slow. We plod along in the initial slow phase with the following framework:

  1. Setting clear, well-defined goals that are sufficiently challenging but also realistic and attainable
  2. Developing a plan to achieve the goal and become immersed in the activity to achieve the goal.
  3. Constantly measuring progress with appropriate metrics and readjusting the goal when milestones are met.
  4. Sustaining involvement by wholeheartedly committing to the goal and concentrating on the task. It is the depth of involvement in the activity that will remove distractions and keep the involvement sustainable.

Then voila, in a blink of an eye and without warning, we emerge with new symmetries associated with a phase transition. In French, the verb essayNew_Pyramid.pnger means to try, to attempt, to embark upon. I hope to use these essays in an attempt to uncover personal phase transitions and new freedoms with the goal of moving up self-actualization and even self-transcendence. As the historian, Will Durant so eloquently stated, “the only real revolution is in the enlightenment of the mind and the improvement of character, the only real emancipation is individual.”